[EM] Example of Condorcet Missing the Highest Utility Center Candidate

[Forest Simmons]

Juho,

thanks for your insights.

In your excellent example, candidate D appears to be the IA-MPO winner,
especially if we define implicit approval as "ranked above bottom."

Forest

On Fri, Jun 5, 2015 at 12:03 AM, Juho Laatu <juho4880 at yahoo.com> wrote:

> One solution for this problem would be to use some rated method. If every
> voter votes according to his travel distances to each candidate center we
> could get ideal results. I mean that actually we are discussing here
> indirectly whether to use ranked or rated methods.
>
> (In the example one could mandate each voter to vote based on the distance
> (in the rated method based election), or calculate the results based on the
> addresses of the voters, i.e. without having an election. This way we could
> get rid of any possible strategies.  :-) )
>
> When compared to the rated methods, (plain) Condorcet methods focus only
> on counting the majorities, not the strength of opinions. In this example
> any two 33 voter groups could form a clear majority. They could agree to
> vote together to make the center between them the winner. Any sensible
> argument against the third 33 voter group could be a sufficient reason (for
> the two 33 groups) to do so.
>
> One could say that Condorcet methods aim at electing stable winners. They
> try to seek a winner that will not be disliked by some clear majority. (I'm
> vague here because the behaviour of different Condorcet methods is somewhat
> different.) If you would elect C, there could easily be some majority
> alliance that would be interested in trying to change the elected center to
> another center. If you elect Mx, the outcome is probably more stable.
>
> One can study this example also from strategic voting point of view. I
> guess the given votes are quite stable and there are no obvious strategies
> to improve one's (distance based) expected outcome. Condorcet could however
> make it possible to strategically make the result worse in the sense that
> the voters could reduce their expected outcome in terms of distance but
> make the expected outcome better in the sense that the whole society would
> benefit of it. I mean that many voters could see that C is obviously in
> some sense best for the society, and they could therefore rank C first in
> their ballots. No harm done and no risks doing so, if the voters truly
> prefer a solution that is good for all, and not just good for them
> personally. The point here is that Condorcet does not force them to make
> decisions that they consider stupid. If some solution looks stupid to us in
> some example, maybe the voters would see that stupidity too, and vote
> accordingly (changing their preferences to something more sensible).
>
> Juho
>
> P.S. I'm ok with electing Condorcet losers in some (extreme) scenarios. As
> I already said, Condorcet methods tend to seek stable solutions. In the
> following example the Condorcet loser (D) is disliked only very mildly in
> the pairwise comparisons, while all the others have a strong opposition
> against them (in favour of changing them to some other candidate).
> 17 A>B>D>C
> 16 A>D>B>C
> 17 B>C>D>A
> 16 B>D>C>A
> 17 C>A>D>B
> 16 C>D>A>B
>
>
>
> On 05 Jun 2015, at 05:11, Forest Simmons <fsimmons at pcc.edu> wrote:
>
>
> Suppose that a town with 100 voting citizens has 33 voters residing at
> each of the three vertices of an equilateral triangle (with two mile sides,
> say), and one voter residing within two hundred yards of the the center of
> the triangle.
>
>
> Proposed sites for the new community center are M1, M2, and M3, at the
> respective midpoints of the three sides of the triangle, as well as site C
> at the center of the triangle’ a couple of hundred yards from the lone
> voter that we just mentioned.
>
>
> Assuming that voters prefer closer sites over more distant sites the
> preferences are
>
>
> 33 M1=M2>C
>
> 33 M1=M3>C
>
> 33 M2=M3>C
>
> 01 C
>
> Note that C is the Condorcet Loser, since each of the M’s beats C pairwise
> by almost a two-thirds majority, 66 to 34.
>
>
> On the other hand, C is the IA winner with 100 percent implicit approval.
>
>
> Candidate C is also the IA-MPO winner with a score of 100-66, compared
> with 66-33 for the other alternatives.
>
>
> How about average distance of voters from each of the alternatives?
>
> The average distance to alternative C is 0.66 times the square root of
> three miles, or about 1.14 miles.
>
>
> The average distance to any of the M’s is about 1.24 miles.
>
>
> If the M’s were moved directly away from their midpoint positions to a
> position nearly twice as far from the center as the midpoint position, the
> preference schedule based on distances would not change, but the average
> distance from voter to any of the M’s would go up from about 1.24 to
> about 1.52 miles, more than 33 percent farther than the average distance to
> C.
>
>
> Think of it: the center location is about 33 percent better on average.  It
> cuts the distance in half for the faction that ends up furthest from the
> winning M, and doesn’t give a lopsided solution where 33 voters have to go
> twice as far (forever after) as the other 66 voters on the vertices of the
> triangle.  It is the geometrical center solution and the approval
> solution, but it is the Condorcet Loser.
>  ----
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>
>
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